1. Field of the Invention
The present invention relates to a method of measuring the gas transmission rate of a plastic film and a measuring apparatus for the method, which measure the transmission rates of various gases which are transmitted through plastic films.
2. Description of the Related Art
Plastic films have been used in a wide range of applications including food storage containers, and new materials for such films have been developed one after another. Gas permeability is an important property in understanding the performance and quality of these films, and hence measuring apparatuses based on various schemes have been developed and commercialized in various countries.
There are three known methods of measuring gas transmission rates for general gases: the differential pressure method, the isobaric method, and the small bag method. For water vapor, the cap method, the moisture sensor method, the infrared sensor method, and the dish method are known.
The gas transmission rates of films are general measured by using the differential pressure method or the isobaric method defined in JIS (Japanese Industrial Standard) (Testing method for gas transmission rate through plastic film and sheeting: JIS K 7126, testing methods for water vapor transmission rate of plastic film and sheeting; JIS K 7129, method of permeability test for moisture proof packing case; and JIS Z 02222, and testing methods for determination of the water vapor transmission rate of moisture-proof packaging materials: JIS Z 0208).
In the differential pressure method, one of the two portions separated by a test piece is kept in a vacuum, and a test gas is introduced into the other portion, thereby obtaining a gas transmission rate on the basis of an increase in pressure on the low-pressure side. In the isobaric method, a test gas is supplied to one of the two portions separated by a test piece while a carrier gas is flowed in the other portion at equal pressure, and the amount of gas transmitted is measured by some kind of gas detector or gas chromatograph. Measuring apparatuses based on the differential pressure method and the isobaric method have been developed and commercialized for a long time. In either of the methods, the surrounding of a test piece attached to a measuring portion must completely be sealed, and measuring apparatuses themselves are complicated.
The measuring method based on the small bag method was made public (Toshio Inoue and Takasuke Ishitani, xe2x80x9cChanges in Oxygen Concentration and Volume over Time in Gas Purge Packagingxe2x80x9d, Packaging Study Vol. 11, No. 1 (1990), pp. 21-27). According to this method, a change in gas concentration in the bag and a change in the volume of the bag are checked. When a film subjected to gas transmission rate measurement is to be actually used as a product, the film is often processed into a bag-like airtight container and, for example, food is sealed into the container. The small bag method allows tests and evaluations in accordance with actual usage including the structures of bags, and hence is considered to have a wide range of applications.
In this method, however, both a change in gas concentration and a change in bag volume must be measured. A volume change is obtained from, for example, an increase in water level upon sinking a bag into the water, whereas a concentration change is obtained by using, for example, a gas chromatograph. There is therefore no merit in directly measuring an airtight bag, and no measuring apparatus based on this method has been commercialized.
Either of the cap method and the dish method which use no gas sensor is a method of measuring an increase in the weight of a hygroscopic material due to water vapor that is transmitted into a container or bag; measurement is limited to water vapor.
As described above, the conventional methods of measuring the gas transmission rates of plastic films demand complicated procedures and complicated measuring apparatuses.
The present invention has been made in consideration of the above situation, and has as its object to provide a method of measuring the gas transmission rate of a plastic film, which requires only simple measurement preparations and procedures and exhibits very high measurement precision as compared with the conventional techniques, a measuring apparatus used for the measuring method, and a gas transmission rate measuring program using the measuring method.
In order to achieve the above object, according to the present invention, there is provided a method of measuring a gas transmission rate of a plastic film, comprising sealing a gas X into a test film bag which is formed by processing a test plastic film into a bag and has a known mass and surface area, measuring a mass of the test film bag in which the gas is sealed, a plurality of numbers of times on the time series, while keeping a temperature constant in a temperature-controlled airtight vessel which is filled with a gas Y different from the gas X so as to make a pressure in the vessel equal to an internal pressure of the test film bag, and obtaining a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) associated with the gas X from a relationship between the measurement results, the mass of the test film bag alone, and the surface area.
More specifically, this method is executed by program processing by an arithmetic processing apparatus on the basis of the following techniques:
(1) A method of measuring a gas transmission rate of a plastic film, in which when a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) kx [mol/m2sPa] of a gas X is known, a transmission rate ky [mol/m2sPa] of a gas Y through a test plastic film is measured, comprising:
preparing a test film bag by processing the test plastic film into a bag, and measuring a mass mf [kg] of the test film bag alone and a total surface area A [m2] associated with gas transmission in advance;
sealing the gas X into the test film bag at a density xcfx81x, and measuring masses m0 [kg], m1 [kg], and m2 [kg] of the test film bag in which the gas is sealed at least at times t0 [s], t1 [s], and t2 [s] in an airtight vessel which is filled with the gas Y at a density xcfx81y so as to set a pressure P [Pa] equal to an internal pressure of the test film bag and in which a temperature is kept constant at a measurement temperature T [K];
obtaining volumes Vx0, Vx1, and Vx2 of the gas X in the test film bag at times t0, t1, and t2 from
Vx0=(m0xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx1=(m1xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx2=(m2xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
obtaining xcexx by substituting the obtained results into the following equation for obtaining xcexx:
xcexx={a(t1xe2x88x92t0)xe2x88x92b(t2xe2x88x92t0)}/(aVx1xe2x88x92bVx2xe2x88x92cVx0)
for
a=log Vx0xe2x88x92log Vx2
b=log Vx0xe2x88x92log Vx1
c=log Vx1xe2x88x92log Vx2
and
computing
ky=(xcexxKx2+Kx)/(RTA)
where R is a gas constant and Kx=kxRTA
thereby obtaining the transmission rate ky of the gas Y when the transmission rate kx is known.
(2) A method of measuring a gas transmission rate of a plastic film, in which when a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) ky [mol/m2sPa] of a gas Y is known, a transmission rate kx [mol/m2sPa] of a gas X through a test plastic film is measured, comprising:
preparing a test film bag by processing the test plastic film into a bag, and measuring a mass mf [kg] of the test film bag alone and a total surface area A [m2] associated with gas transmission in advance;
sealing the gas X into the test film bag at a density xcfx81x, and measuring masses m0 [kg], m1 [kg], and m2 [kg] of the test film bag in which the gas is sealed at least at times t0 [s], t1 [s], and t2 [s] in an airtight vessel which is filled with the gas Y at a density xcfx81y so as to set a pressure P [Pa] equal to an internal pressure of the test film bag and in which a temperature is kept constant at a measurement temperature T [K];
obtaining volumes Vx0, Vx1, and Vx2 of the gas X in the test film bag at times t0, t1, and t2 from
Vx0=(m0xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx1=(m1xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
xe2x80x83Vx2=(m2xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
obtaining xcexx by substituting the obtained results into the following equation for obtaining xcexx:
xcexx={a(t1xe2x88x92t0)xe2x88x92b(t2xe2x88x92t0)}/(aVx1xe2x88x92bVx2xe2x88x92cVx0)
for
a=log Vx0xe2x88x92log Vx2
b=log Vx0xe2x88x92log Vx1
c=log Vx1xe2x88x92log Vx2
and
when xcexx greater than 0, computing
kx={xe2x88x921+(1+4xcexxKy)1/2}/(2xcexxRTA)
where R is a gas constant and Kx=kxRTA
and when xcexx less than 0, computing
kx={xe2x88x921xc2x1(1+4xcexxKy)1/2}/(2xcexxRTA)
thereby obtaining the transmission rate kx of the gas X when the transmission rate ky is known.
(3) A method of measuring a gas transmission rate of a plastic film, in which when a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) ky [mol/m2sPa] of a gas Y is known, a transmission rate kx [mol/m2sPa] of a gas X through a test plastic film (kx greater than  greater than ky) is measured, comprising:
preparing a test film bag by processing the test plastic film into a bag, and measuring a mass mf [kg] of the test film bag alone and a total surface area A [m2] associated with gas transmission in advance;
sealing the gas X into the test film bag at a density xcfx81x, and measuring masses m0 [kg], m1 [kg], and m2 [kg] of the test film bag in which the gas is sealed at least at times t0 [s], t1 [s], and t2 [s] in an airtight vessel which is filled with the gas Y at a density xcfx81y so as to set a pressure P [Pa] equal to an internal pressure of the test film bag and in which a temperature is kept constant at a measurement temperature T [K];
obtaining volumes Vx0, Vx1, and Vx2 of the gas X in the test film bag at times t0, t1, and t2 from
Vx0=(m0xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx1=(m1xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx2=(m2xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
obtaining xcexx by substituting the obtained results into the following equation for obtaining xcexx:
xcexx={a(t1xe2x88x92t0)xe2x88x92b(t2xe2x88x92t0)}/(aVx1xe2x88x92bVx2xe2x88x92cVx0)
for
a=log Vx0xe2x88x92log Vx2
b=log Vx0xe2x88x92log Vx1
c=log Vx1xe2x88x92log Vx2
and
computing
kx=xe2x88x921/(xcexxRTA)
where R is a gas constant
thereby approximating the transmission rate kx of the gas X when the transmission rate ky (kx greater than  greater than ky) is known.
(4) A method of measuring a gas transmission rate of a plastic film, in which when a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) ky [mol/m2sPa] of a gas Y is known, a transmission rate kx [mol/m2sPa] of a gas X through a test plastic film (kx greater than  greater than ky) is measured, comprising:
preparing a test film bag by processing the test plastic film into a bag, and measuring a mass mf [kg] of the test film bag alone and a total surface area A [m2] associated with gas transmission in advance;
sealing the gas X into the test film bag at a density xcfx81x, and measuring masses m0 [kg] and m1 [kg] of the test film bag in which the gas is sealed at least at times t0 [s] and t1 [s] in an airtight vessel which is filled with the gas Y at a density xcfx81y so as to set a pressure P [Pa] equal to an internal pressure of the test film bag and in which a temperature is kept constant at a measurement temperature T [K];
obtaining volumes Vx0 and Vx1 of the gas X in the test film bag at times t0 and t1 from
Vx0=(m0xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx1=(m1xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
and
computing
kx=(Vx1xe2x88x92Vx0)/{(t1xe2x88x92t0)RTA}
where R is a gas constant
thereby approximating the transmission rate kx of the gas X when the transmission rate ky (kx greater than  greater than ky) is known.
(5) A method of measuring a gas transmission rate of a plastic film, which measures a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) kx [mol/m2sPa] of a gas X and a transmission rate ky [mol/m2sPa] of a gas Y through a test plastic film, comprising:
preparing first and second test film bags each obtained by processing the test plastic film into a bag, and measuring masses mf [kg] and mfxe2x80x2 [kg] of the respective test film bags alone and total surface areas A [m2] and Axe2x80x2 [m2] associated with gas transmission in advance;
sealing the gas X into the first test film bag at a density xcfx81x, and measuring masses m0 [kg], m1 [kg], and m2 [kg] of the first test film bag in which the gas is sealed at least at times t0 [s], t1 [s], and t2 [s] in an airtight vessel which is filled with the gas Y at a density xcfx81y so as to set a pressure P [Pa] equal to an internal pressure of the first test film bag and in which a temperature is kept constant at a measurement temperature T [K];
sealing the gas Y into the second test film bag at a density xcfx81yxe2x80x2, and measuring masses m0xe2x80x2 [kg], m1xe2x80x2 [kg], and m2xe2x80x2 [kg] of the second test film bag in which the gas is sealed at least at times t0xe2x80x2 [s], t1xe2x80x2 [s], and t2xe2x80x2 [s] in an airtight vessel which is filled with the gas X at a density xcfx81xxe2x80x2 so as to set a pressure Pxe2x80x2 [Pa] equal to an internal pressure of the second test film bag and in which a temperature is kept constant at a measurement temperature Txe2x80x2 (Txe2x80x2=T) [K];
obtaining volumes Vx0, Vx1, and Vx2 of the gas X in the first test film bag at times t0, t1, and t2 from
Vx0=(m0xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx1=(m1xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
Vx2=(m2xe2x88x92mf)/(xcfx81xxe2x88x92xcfx81y)
obtaining xcexx by substituting the obtained results into the following equation for obtaining xcexx:
xcexx={a(t1xe2x88x92t0)xe2x88x92b(t2xe2x88x92t0)}/(aVx1xe2x88x92bVx2xe2x88x92cVx0)
for
a=log Vx0xe2x88x92log Vx2
b=log Vx0xe2x88x92log Vx1
c=log Vx1xe2x88x92log Vx2
obtaining volumes Vy0xe2x80x2, Vy1xe2x80x2, and Vy2xe2x80x2 of the gas Y in the first test film bag at times t0xe2x80x2, t1xe2x80x2, and t2xe2x80x2 from
Vy0xe2x80x2=(m0xe2x80x2xe2x88x92mfxe2x80x2)/(xcfx81yxe2x80x2xe2x88x92xcfx81xxe2x80x2)
xe2x80x83Vy1xe2x80x2=(m1xe2x80x2xe2x88x92mfxe2x80x2)/(xcfx81yxe2x80x2xe2x88x92xcfx81xxe2x80x2)
Vy2xe2x80x2=(m2xe2x80x2xe2x88x92mfxe2x80x2)/(xcfx81yxe2x80x2xe2x88x92xcfx81xxe2x80x2)
obtaining xcexy by substituting the obtained results into the following equation for obtaining xcexy:
xcexy={axe2x80x2(t1xe2x80x2xe2x88x92t0xe2x80x2)xe2x88x92bxe2x80x2(t2xe2x80x2xe2x88x92t0xe2x80x2)}/(axe2x80x2Vy1xe2x80x2xe2x88x92bxe2x80x2Vy2xe2x80x2xe2x88x92cxe2x80x2Vy0xe2x80x2)
for
axe2x80x2=log Vy0xe2x80x2xe2x88x92log Vy2xe2x80x2
bxe2x80x2=log Vy0xe2x80x2xe2x88x92log Vy1xe2x80x2
cxe2x80x2=log Vy1xe2x80x2xe2x88x92log Vy2xe2x80x2
when xcexx greater than 0 and xcexy less than 0, computing
kx=xe2x88x921/(xcexxRTA)+1/{RT(xe2x88x92xcexxxcexyAAxe2x80x2)1/2}
ky=xe2x88x921/(xcexyRTAxe2x80x2)xe2x88x921/{RT(xe2x88x92xcexxxcexyAAxe2x80x2)1/2}
where R is a gas constant
and
when xcexx less than 0 and xcexy greater than 0, computing
kx=xe2x88x921/(xcexxRTA)xe2x88x921/{RT(xe2x88x92xcexxxcexyAAxe2x80x2)1/2}
ky=xe2x88x921/(xcexyRTAxe2x80x2)+1/{RT(xe2x88x92xcexxxcexyAAxe2x80x2)1/2}
thereby obtaining the transmission rate kx of the gas X and the transmission rate ky of the gas Y.
(6) When a saturation vapor pressure of the gas X is lower than atmospheric pressure, the pressure in the airtight vessel is reduced to make a saturation vapor pressure in the test film bag become higher than the pressure in the airtight vessel.
(7) A method of measuring a gas transmission rate of a plastic film, which measures a transmission rate (a value representing the number of moles of a gas transmitted through a test piece with a unit area in a unit time at a unit partial pressure difference) kx of a gas X, through a test plastic film, whose saturation vapor pressure is lower than atmospheric pressure at room temperature, comprising:
preparing a test film bag by processing the test plastic film into a bag, and measuring a mass mf [kg] of the test film bag alone and a total surface area A [m2] associated with gas transmission in advance;
sealing the gas X into the test film bag while part of the gas is a liquid such that the vapor pressure is set in a saturate state, and allowing measurement of a mass of the test film bag in which the gas is sealed in an airtight vessel which is filled with a gas Y whose saturation vapor pressure is higher than atmospheric pressure at room temperature and in which a measurement temperature can be arbitrarily controlled;
measuring a mass m0 [kg] of the test film bag in which the gas is sealed in state 0 in which an internal temperature of the airtight vessel is set to T0 [K] and a pressure is set to P0 [Pa] equal to atmospheric pressure (a saturation vapor pressure Px0 [Pa] of the gas X, a density xcfx81x of the gas X, and a density xcfx81y of the gas Y);
measuring a mass m1 [kg] of the test film bag in which the gas is sealed in state 1 in which an internal temperature of the airtight vessel is set to T1 [K] (a pressure P1 [Pa], a saturation vapor pressure Px1 [Pa] of the gas X, a density xcfx81x1 of the gas X, and a density xcfx81y1 of the gas Y);
measuring a mass m2 [kg] of the test film bag in which the gas is sealed in state 2 after a lapse of a predetermined period of time t [s] since state 1 while the internal temperature T1 [K] of the airtight vessel (the pressure P1 [Pa], the saturation vapor pressure Px1 [Pa] of the gas X, the density xcfx81x1 of the gas X, and the density xcfx81y1 of the gas Y) is maintained;
after measurement in state 2, measuring a mass m3 [kg] of the test film bag in which the gas is sealed in state 3 in which the internal temperature of the airtight vessel is set to T3 [K] (a pressure P3 [Pa] and a saturation vapor pressure Px3 [Pa]);
obtaining a total mass of the liquid and gas in the test film bag in state 1 from
mx1+xcfx81x1Vx1=m1xe2x88x92mf+(m0xe2x88x92m1)(P0/Px0xe2x88x921)/(P0/Px0xe2x88x92P1/Px1)
obtaining the total mass of the liquid and gas in the test film bag in state 2 from
mx2+xcfx81x2Vx2=m3xe2x88x92mf+(m2xe2x88x92m3)(P1/Px2xe2x88x921)/(P1/Px2xe2x88x92P3/Px3)
and
obtaining the transmission rate kx of the gas X by substituting the computation results into the following equation and computing the equation:
kx={(mx1+xcfx81x1Vx1)xe2x88x92(mx2+xcfx81x2Vx2)}/(tPxA)
(8) In measurement of the mass, a measured weight value is corrected on the basis of a gravitational acceleration at a measurement place.
A measuring apparatus used to execute the above measuring method comprises a constant temperature vessel which is used as the airtight vessel and includes internal temperature control means and gas filling means, an electronic balance which is mounted in the constant temperature vessel and measures a mass of a test film bag in which the gas is sealed, and an arithmetic processing unit in which an arithmetic processing program in any one of (1) to (7) is installed in advance and which obtains a transmission rate value of a test gas by inputting the measurement results.
The above measuring apparatus further comprises measurement automating means for acquiring a measured mass value at a predetermined time from the electronic balance by setting an internal temperature in the constant temperature vessel to a measurement temperature through the internal temperature control means.
Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter.